A dual finite fields algorithm for elliptic curve cryptosystem and FPGA implementation

A dual finite fields algorithm for elliptic curve cryptosystem (ECC) is presented. It can be used in two kinds of finite fields, which are Galois fields GF (p) and GF (2m) for arbitrary prime numbers and irreducible polynomials respectively. An arithmetic unit, which can perform all dual Galois fields' arithmetic operations, including addition, subtraction, multiplication, squaring, inversion and division, is designed for the ECC. Furthermore, the authors describes a FPGA implementation of ECC. It can efficiently handle requests for different ECC key length and different curves in GF (p) and GF (2m).EI06871-8764